Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<cmath>
#include<iostream>
#define N 210000
using namespace std;
int a[N],p[N],f[N],t[N],n;
bool cal(int i,int j,int k)
{
	return (p[i]<p[j])&&(p[j]<p[k]);
}
bool check(int i,int j,int k)
{
	return cal(i,j,k)|cal(j,k,i)|cal(k,i,j);
}
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%d",&a[i]),p[a[i]]=i;
	for(int i=n-1;i>=1;i--)
		if(t[i+1]==0)
		{
			if(p[i]>p[i+1]) t[i]=1,f[i]=i+1;
		}
		else
		{
			if(check(i,i+1,f[i+1])) t[i]=t[i+1],f[i]=f[i+1];
			else t[i]=t[i+1]+1,f[i]=i+1;
		}
	printf("%d\n",t[1]);
	return 0;
}